Title: Determining Perpendicular Magnetic Anisotropy in Fe/MgO/Fe Magnetic Tunnel Junction: A DFT-Based Spin-Orbit Torque Method

Abstract: In our JunPy package, we have combined the first-principles calculated self-consistent Hamiltonian with divide-and-conquer technique to successfully determine the magnetic anisotropy (MA) in an Fe/MgO/Fe magnetic tunnel junction (MTJ). We propose a comprehensive analytical derivation to clarify the crucial roles of spin-orbit coupling that mediates the exchange and spin-orbit components of spin torque, and the kinetic and spin-orbit components of spin current accumulation. The angular dependence of cumulative spin-orbit torque (SOT) indicates a uniaxial MA corresponding to the out-of-plane rotations of magnetic moments of the free Fe layers. Different from the conventional MA energy calculation and the phenomenological theory for a whole MTJ, our results provide insight into the orbital-resolved SOT for atomistic spin dynamics simulation in emergency complex magnetic heterojunctions.